Requiring Bluetooth and an Internet connection on your phone suggests that that's exactly what they removed on their side. Quite clever, if true – why pay for network connectivity if you can just piggy back on your customers'? (Nevermind those customers without a smart phone and data plan...)
Let's put it like this: The old ones (with a display) definitely do, because they can send email notifications. I would be very much surprised if the new ones didn't. The main reason for requiring the app isn't connectivity to the outside world, it is that they can save money on the terminal screens, which get vandalized frequently in some areas. The internet connection is probably a fraction of the cost of replacing those touch screens every few months.